Question

Simplify

$3\frac{1}{2} + 5\frac{2}{3} - 4\frac{7}{6}$

• A. 8
• B. 12
• C. 4
• D. 2

Answer 1

Answer:

C. 4

The given expression is:

$3\frac{1}{2} + 5\frac{2}{3} - 4\frac{7}{6}$

Step 1: Convert the mixed fractions into improper fractions:

* $3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}$

* $5\frac{2}{3} = \frac{(5 \times 3) + 2}{3} = \frac{17}{3}$

* $4\frac{7}{6} = \frac{(4 \times 6) + 7}{6} = \frac{31}{6}$

Now, the expression becomes:

$\frac{7}{2} + \frac{17}{3} - \frac{31}{6}$

Step 2: Find a common denominator:

The Least Common Multiple (LCM) of the denominators 2, 3, and 6 is 6.

Step 3: Convert each fraction to have the common denominator of 6:

* $\frac{7 \times 3}{2 \times 3} = \frac{21}{6}$

* $\frac{17 \times 2}{3 \times 2} = \frac{34}{6}$

* $\frac{31}{6}$ (remains the same)

Step 4: Perform the addition and subtraction:

$\frac{21 + 34 - 31}{6}$

$\frac{55 - 31}{6} = \frac{24}{6}$

Dividing 24 by 6 gives:

$24 \div 6 = \mathbf{4}$